I'll politely disagree with the above posters. My son didn't sit on his own (nothing behind him, etc) until he was 7 months or so, but he ate in his Bumbo and on my lap a bunch. I figure if he had the motor skills to pick up, chew, and swallow the food, it doesn't matter if there's something supporting his back. After all, I would much rather sit in a chair with a back too.
Can you give him a spoon to play with or something while he's sitting with you at the table? My son was doing the same thing around 5 months. I actually put some pear strips out in front of him at 5.5 months just so he could get used to the idea and had to take them away when he picked one up and put it in his mouth!
FYI we have only used a Bumbo and later a Fisher Price booster seat. Waiting until they can sit up (more or less) is alot more cost effective ;-)